Re: An example ?
"With drive-by infections, it is enough to simply visit a website to infect a computer with malware. Visitors don't need to start a download or install anything - the website does this automatically!"
My browser will not automatically download anything, without asking me where it should save it first. What kind of browser are you using that would do this? An idiotic one by the sound of it.
"Yet If a browser has a relevant safety gap, such scripts can access a user's computer directly. This therefore enables malware to move from the server to the browser, and via the security gap to the user's computer, without any conscious action by the website visitor at all."
Again, it's a problem with the browser, and you should change your browser.
The reason I mentioned ActiveX is because that is the biggest hole in your browser, then comes Java (I do not allow this to run), then Flash (run with permission). That leaves JavaScript with Ajax or other call-to-the-server methodologies, which can only write to the web page, open new web pages, or write to cookies. None of those compromise a PC.
JavaScript and HTML are not capable of infecting your PC. Buggy browsers, ActiveX, Java and Flash, however, can. The article is talking about Javascript. Now, go back to sleep!